Semi–Blind Model (In) Validation with Applications to Texture Classification

This paper addresses the problem of model (in)validation of linear discrete–time (LTI) models subject to unstructured LTI uncertainty, using frequency–domain data corrupted by additive noise. Contrary to the case usually considered in the (deterministic) invalidation literature, here the input to the system has an unknown phase. This problem arises naturally for instance in the context of validating systems subject to unknown time–delays, or in cases where only the spectral power density of the (in this case stochastic) input is known. It can be shown that this leads to a generically NP hard minimization problem. The main result of this paper is an efficient, LMI based convex relaxation of the problem. These results are illustrated with a non–trivial problem: classification of textured images.